1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Classical Mechanics Q: trajectory of q in B and E fields

  1. Feb 2, 2016 #1
    Hi all! I'm super lost on this hw question. I tried asking the professor but was kind of brushed to the side. My vector calculus knowledge is pretty limited (I had an unfortunately experience in that class). Anybody have any ideas on how to go about solving for this?

    It's a problem out of Classical Mechanics-by Taylor, Chapter 2 Section 5

    2.55 ***

    A charged particle of mass m and positive charge q moves in uniform electric and magnetic fields,
    E pointing in the y direction and B in the z direction (an arrangement called "crossed E and B
    fields"). Suppose the particle is initially at the origin and is given a kick at time t= 0 along the x axis
    with Vx = Vxo (positive or negative).
    (a) Write down the equation of motion for the particle and resolve it into its three components. Show that the motion remains in the plane z =0.

    (b) Prove that there is a unique value of Vxo, called the drift speed Vdr, for which the particle moves undeflected through the fields. (This is the basis of velocity selectors, which select particles traveling at one chosen speed from a beam with many different speeds.)

    (c) Solve the equations of motion to give the particle's velocity as a function of t, for arbitrary values of
    Vx0. [Hint: The equations for (Vx, Vy) should look very like Equations (2.68) except for an offset of Vx
    by a constant. If you make a change of variables of the form Ux = Vx —Vdr
    and Uy=Vy, the equations for (Ux, Uy) will have exactly the form (2.68), whose general solution you know.]
    (attached is equation 2.68)

    (d) Integrate the velocity to find the position as a function of t and sketch the trajectory for various values of Vxo

    Attached Files:

  2. jcsd
  3. Feb 2, 2016 #2
    Just divide the E and B apart, and then...use calculus, finally you may put them together again. (I'm afraid that calculus is necessary in this question.) (I'm just a CN high school student so I feel sorry that I have no idea of solving the problem.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted